Problem: Given $ m \angle BOC = 4x - 39$, and $ m \angle AOB = 6x + 49$, find $m\angle BOC$. $O$ $A$ $C$ $B$
Explanation: From the diagram, we see that together ${\angle AOB}$ and ${\angle BOC}$ form ${\angle AOC}$ , so $ {m\angle AOB} + {m\angle BOC} = {m\angle AOC}$ Since $\angle AOC$ is a straight angle, we know ${m\angle AOC = 180}$ Substitute in the expressions that were given for each measure: $ {6x + 49} + {4x - 39} = {180}$ Combine like terms: $ 10x + 10 = 180$ Subtract $10$ from both sides: $ 10x = 170$ Divide both sides by $10$ to find $x$ $ x = 17$ Substitute $17$ for $x$ in the expression that was given for $m\angle BOC$ $ m\angle BOC = 4({17}) - 39$ Simplify: $ {m\angle BOC = 68 - 39}$ So ${m\angle BOC = 29}$.